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I'm using LISREL. On my printouts under LISREL 7, I used to get a statistic called "Total coefficient of determination for structural equations". I can't seem to get it when I use LISREL 8. How can I get this information using LISREL 8?
The authors of LISREL 8 decided not to include this statistic as part of the available LISREL output. This means that you must compute it based on other portions of the LISREL output.
The formula for the total coefficient of determination for structural equations is:
||PSI||/||cov_eta||
where ||PSI|| is the determinant of the psi (LISREL PS) matrix and ||cov_eta|| is the determinant of the covariances of the LISREL eta matrix.
You can compute the value of the total coefficient of determination for structural equations using any software program which permits matrix manipulation and matrix operations. One such program is SAS/IML.
Suppose you have the following LISREL program and output (edited to conserve space).
Stability of Alienation
! lisdemo3.ls7
! See LISREL8 manual, p. 207
! Chapter 6.4: Two-wave models
! Program to generate data for SAS IML program ! To calculate total coeff
of determination for ! structural equations
! A LISREL7-generated printout yields a coefficient ! of determination,
squared, for structural equations ! of .345. The SAS IML program should
yield the same ! value.
DA NI=6 NO=932
LA
ANOMIA67 POWERL67 ANOMIA71 POWERL71 EDUC SEI CM FI=ex64.cov
MO NY=4 NX=2 NE=2 NK=1 TE=SY,FI TD=SY,FI PS=FU PA LY
0 0
1 0
0 0
0 1
VA 1.0 LY(1,1) LY(3,2)
PA LX
0
1
VA 1.0 LX(1,1)
FR TE(1,1) TE(2,2) TE(3,3) TE(4,4) TD(1,1) TD(2,2) PS(2,1) OU RS EF
Stability of Alienation
NUMBER OF INPUT VARIABLES 6
NUMBER OF Y - VARIABLES 4
NUMBER OF X - VARIABLES 2
NUMBER OF ETA - VARIABLES 2
NUMBER OF KSI - VARIABLES 1
NUMBER OF OBSERVATIONS 932
Stability of Alienation
COVARIANCE MATRIX TO BE ANALYZED
ANOMIA67 POWERL67 ANOMIA71 POWERL71 EDUC SEI
-------- -------- -------- -------- -------- --------
ANOMIA67 11.83
POWERL 6.95 9.36
ANOMIA71 6.82 5.09 12.53
POWERL71 4.78 5.03 7.50 9.99
EDUC -3.84 -3.89 -3.84 -3.62 9.61
SEI -2.19 -1.88 -2.17 -1.88 3.55 4.50
(output deleted)
COVARIANCE MATRIX OF ETA AND KSI
ETA 1 ETA 2 KSI 1
-------- -------- --------
ETA 1 7.82
ETA 2 6.22 8.83
KSI 1 -4.09 -4.04 6.66
(output deleted)
PSI
ETA 1 ETA 2
-------- --------
ETA 1 5.31
(.47)
11.23
ETA 2 3.74 6.38
(.36) (.54)
10.48 11.83
You would then take the output from the PSI matrix and the output from the ETA portion of the COVARIANCE MATRIX OF ETA AND KSI and place these in the following SAS IML program.
* Begin sample program ;
* Program generates Total Coefficient of Determination ;
* for Structural Equations ;
* This statistic was part of the LISREL7 output;
* It is missing from the LISREL8 output ;
* Program uses SAS PROC IML ;
* Input the values from the LISREL PSI matrix from ;
* the LISREL output for variable phi below ;
* Input the values from the LISREL ETA matrix from ;
* the LISREL output for the variable eta below ;
* (Note to include only the ETA by ETA values, not ;
* any ETA by KSI values.
* Example data come from LISREL7 manual, pp. 100-101 ;
OPTIONS ls=72 ;
PROC IML ;
psi={5.31 3.74,
3.74 6.38};
eta={7.82 6.22,
6.22 8.83};
detpsi=DET(psi);
deteta=DET(eta);
ratio=detpsi/deteta;
totalco = 1.00 - ratio ;
PRINT 'Verify accuracy of phi';
PRINT psi ;
PRINT 'Verify accuracy of eta';
PRINT eta ;
PRINT 'Print intermediate calculations' ; PRINT detpsi deteta ratio ;
PRINT 'Total Coefficient of Determination for Structural Equations' ;
PRINT Totalco;
RUN ;
You would alter only the PSI and ETA matrices in your own version of this SAS IML program to have it analyze your own dataset. Notice that these matrices must be fully defined. That is, the LISREL output only includes the lower off-diagonal elements; you must copy the identical values to the upper off-diagonal elements as needed. Also, matrix rows are separated by commas and the matrices are bracketed by the brace symbols { and }.
Use your favorite text editor to recreate this SAS program for analyzing your own data. When you are done with the program, save the file as filename.sas, where filename is a name of your choice.
To submit this program to SAS for processing on the ADS system, type the following command at the host prompt:
/usr/local/sas/sas filename.sas
where filename was the filename you assigned when you saved the file.
SAS will return its results in a file called filename.lst, where filename is the name you specified for your SAS program file.
For example, if you wrote the SAS IML program above and saved it under the name test.sas, you would submit the program to SAS for processing with the command
/usr/local/sas/sas test.sas
and your IML output would appear in the file test.lst in the current working directory on the ADS system.
The output from the sample SAS IML Program above is as follows:
The SAS System 1 17:57 Thursday, July 11, 1996 Verify accuracy of phi PSI 5.31 3.74 3.74 6.38 Verify accuracy of eta ETA 7.82 6.22 6.22 8.83 Print intermediate calculations DETPSI DETETA RATIO 19.8902 30.3622 0.6550975 Total Coefficient of Determination for Structural Equations TOTALCO 0.3449025
If you have further questions, send E-mail to stats@ssc.utexas.edu.